If the Nazis were so oriented on destroying things like art why didn't they destroy British monuments?
The Houses of Parliament was bombed 14 times during the war. The Clocktower (what people mistakenly call Big Ben) was also hit during one of the raids. It blew out the glass on the clockface and damaged the roof. The Commons Chamber was destroyed by fire from an incendiary bomb.
So it's not as if the building and the tower went unscathed, it's just hard to hit targets that specific with the technology of the time.
Most bombing runs took place at night, so they only had London's lights to know what they were bombing.
Bombers were usually situated >1km above their targets.
Bombs dropped from that range have a very low chance of directly hitting their targets (to compare, data from the Vietnam War show that unguided bombs hit their targets 5.5 % of the time, compared to laser guided bombs, which hit targets 50 % of the time).
They would have to calculate when to release the bombs, a very daunting task when you're trying to hit something that takes up 40 sq ft.
I don't know about motive, though.
There were two important instances in which they deliberately targeted monuments of historical or cultural importance. Aside form the aforementioned problems hitting such small targets with WWII technology and often at night, attacking these non-military targets doesn't make a lot of military sense. While there was plenty of collateral damage to historic monuments in conventional or area attacks, the Luftwaffe only started to deliberately target cultural or historic monuments in the UK as a policy of revenge for the increasing strength of the Allied bombing offensive, which had significant collateral damage to German cities.
The V-1's programmed target was Tower Bridge. The rudimentary guidance meant that the missiles went widely off target, but one hit Tower Bridge on 2 August.
And the Luftwaffe did conduct a series of raids targeting famous British landmarks in 1942. The Baedeker Blitz attacked cities for their cultural and historical importance as revenge against the increased destructiveness of the RAF's raids.